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- W2092164416 abstract "Abstract Stute and Wang (1994) considered the problem of estimating the integral Sθ = ∫ θ dF, based on a possibly censored sample from a distribution F, where θ is an F-integrable function. They proposed a Kaplan-Meier integral S n θ to approximate Sθ and derived an explicit formula for the delete-1 jackknife estimate S n(1) θ . S n(1) θ differs from S n θ only when the largest observation, X(n), is not censored (δ(n) = 1 and next-to-the-largest observation, X(n-1), is censored (δ(n-1) = 0). In this note, it will pointed out that when X(n) is censored (δ (n) = 0) S n(1) θ is based on a defective distribution, and therefore S n(1) θ can badly underestimate S θ . We derive an explicit formula for the delete-2 jackknife estimate S n(2) θ . However, on comparing the expressions of S n(1) θ and S n(2) θ , their difference is negligible. To improve the performance of S n(1) θ and S n(2) θ , we propose a modified estimator S n θ according to Efron (1980). Simulation results demonstrate that S n θ is much less biased than S n(1) θ and S n(1) θ and S n(2) θ ." @default.
- W2092164416 created "2016-06-24" @default.
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- W2092164416 date "1998-11-01" @default.
- W2092164416 modified "2023-09-27" @default.
- W2092164416 title "Problems arising from jackknifing the estimate of a Kaplan-Meier integral" @default.
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- W2092164416 doi "https://doi.org/10.1016/s0167-7152(98)00135-7" @default.
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